


proof by contradiction

by taoslefteyelid



Series: birthday fics [1]
Category: EXO (Band), Z.Tao (Musician)
Genre: M/M, but yes happy birthday kika!!!!!! sharing the same birthday with you is an honour, it's about maths turn back now if you didn't like rational numbers, this is weird and i know
Language: English
Status: Completed
Published: 2019-08-19
Updated: 2019-08-19
Packaged: 2020-09-07 18:15:29
Rating: Not Rated
Warnings: No Archive Warnings Apply
Chapters: 1
Words: 1,437
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/20313868
Author URL: https://archiveofourown.org/users/taoslefteyelid/pseuds/taoslefteyelid
Summary: Assumption: Love doesn’t existProof: Sehun.Result: My assumption has been contradicted. Love exists, if only just for him





	proof by contradiction

**Author's Note:**

  * For [superblylovingcoffee](https://archiveofourown.org/users/superblylovingcoffee/gifts).

> HELLO this is another birthday fic and this time it's for kika and!! also for myself bc. we share birthdays jdsalkdf  
anyways happy birthday kika!!!!! i really love you and i hope you enjoyed this dskjajkdf

There comes a point in every student’s life, where one must decide whether they wish to pursue the sciences or the arts. They could also choose to do business, but frankly, if they do so, the probability of them having a soul is infinitesimally small, so for the sake of accuracy, they are not included in this particular telling of events. 

But yes, at this point, if a student does decide to take up the sciences, it is very likely that they will be greeted with one simple problem. A math problem. 

Now, we could debate for hours as to whether math is an art, or a science, but that’s not what this is about. This is about a single math problem. 

_ Prove that the square root of two is irrational. _

Nothing too crazy. The only thing special about it is that this is, in the simplest terms, the first time a student encounters a proof that relies on assumption and contradiction. 

You see, to prove that the square root of 2 is irrational, you start with an assumption. An assumption that the square root of 2  _ is  _ rational.

Here’s how it looks.

_ Assumption: The square root of 2 is rational, such that it can be written in the form p/q, where p and q are rational and q is not 0, where p/q have no common factors. _

_ Proof:  _ _ √2 = a/b _

_ 2 = a _ _ 2 _ _ /b _ _ 2 _

_ a _ _ 2 _ _ = 2 · b _ _ 2  _

_ a = 2k (a is divisible by 2) _

_ 2=(2k) _ _ 2 _ _ /b _ _ 2 _

_ 2=4k _ _ 2 _ _ /b _ _ 2 _

_ 2*b _ _ 2 _ _ =4k _ _ 2 _

_ b _ _ 2 _ _ =2k _ _ 2 _

_b_ _= 2k_ (_b is divisible by 2)_

_ p and q have common factors. _

_ Result: Our assumption has been contradicted. Hence, the square root of 2 is irrational.  _

Huang Zitao first encounters this particular problem in tenth grade math class, and it just so happens that he was using a new notebook that day. Zitao had stared at it for a little too long, thought a little too deeply about it, and somewhere in his little fifteen year old brain, something prompted him to shove his new notebook with that one, singular problem in it back into his backpack, and pull out a different one. 

He had realised why three weeks later, when he’d been stressed to the point of tears over something, and the only thing he could think to do was fish out his notebook from his backpack and turn the page, and scrawl out the problem.

  
  


_ Assumption: My father doesn’t love me _

_ Proof: He yelled at me for saying that I didn’t want to continue wushu anymore. He said I was being ungrateful and indisciplined. He didn’t even try to understand.  _

_ But he drives me to class everyday and he stays awake and works hard to give me what I need and he does the dishes when I say I don’t want to and he sneaks me chocolate when I’m a little too hungry. _

_ Result: My assumption has been contradicted. My father loves me. _

And so it begins.

\---

Zitao is now in college and he still has the same notebook from years ago which he turns to when he can’t think of anything else, when he feels things he shouldn’t, when he looks at himself and realises there’s something in there that he doesn’t like, and he needs a push to fix it. It’s filled with scrawled assumptions about family, life, love, himself. 

_ Assumption: I’m jealous of the new transfer _

_ Proof: He’s very striking, beautiful, almost. He doesn’t have to be commanding, he doesn’t scream “look at me” when he walks into the room. I do that, I’ve been told. He seems a lot gentler, softer, nicer. But I don’t think I want to be him.  _

_ Result: My assumption has been contradicted. I’m not jealous of him.  _

_ I do like him though.  _

\---

The last year of college is here and Zitao can barely believe it, and the new transfer is now his best friend. 

_ Assumption: I don’t want to move in with Sehun _

_ Proof: He’s messy and he’s always slinking around in the middle of the night, and I know he’ll never do laundry. He’s cute and he knows it and he’ll use it against me, but god, holy shit, I’ll miss him when college is over, and I can’t do this without him, I can’t. I’ll miss him too much, and I can do laundry myself. _

_ Result: My assumption has been contradicted. I do want to move in with Sehun. _

\---

_ Assumption: I’m not going to get into this studio _

_ Proof: I never had music theory as a major, it was only a hobby. I don’t think I’m that good at mastering music, and my rapping needs work and I wish I payed more attention in guitar class. LOEY studios only takes the best.  _

_ My portfolio is impressive though. Besides, my interview went perfectly, me and Chanyeol hit it off really well.  _

_ Sehun likes my music. _

_ Result: My assumption has been contradicted. I’ll get into this studio. _

\---

Zitao doesn’t know when it happens. Maybe it’s when Sehun picks him up from work at the studio that one time and he’s brought Zitao’s favourite coffee along, or maybe it’s when Sehun sleepwalks straight into Zitao’s bed and Zitao lets him stay, even though he’s strong enough to carry Sehun back to his room. He doesn’t know how it happens. 

But it does.

_ Assumption: I’m not in love with my best friend _

_ Proof: His hands are always too dry and he calls me to kill spiders even though I’m more scared of them than he is but god I’d do anything for him, fuck, holy shit, I’d do anything for him, he could ask for anything and I wouldn’t think twice. He smiles at me like I’ve given him the world in his hands and his hands get cold so he sticks them in mine and does this little impatient dance as I try to warm him up and he’s pretty when he laughs but he’s pretty when he cries too but I hate it when he cries. That one time he got drunk and sat down in my lap and refused to go anywhere until I carried him and that time right in the beginning when I ran five blocks so that I could get to Starbucks in time to get coffee with him and he laughed at me and the time I fell sick and he fed me the worst chicken soup I’ve ever had in my life while talking about how stupid I am. He’s so lovely and beautiful and he deserves everything in the world and I want to see him smile at me first thing in the morning and it’s four am and I’ve been having a crisis and even then all I want is for him to give me one of his stupid backhugs I can’t do this I can’t do this I can’t do this  _

_ Result: This is hopeless _

\---

The next few pages are ripped out, as if Zitao has had multiple crises over the same thing and is writing about them again and again but his pen is too confused and panicked, and it gouges through the paper till the page is unusable. 

_ Assumption: Sehun didn’t mean to kiss me _

_ Proof: He was crying and his hands were shaking, and all I did was hold him through it, and then he looked up at me and his eyes were so hopeful my heart broke, and he kissed me, he kissed me first, and I kissed back, and he let me kiss him, and then when I pulled away he looked so scared and he keeps knocking on the door right now and apologising and i don’t know i don’t know i don’t know what do i do? _

_ Result: I hope my assumption is wrong. I might just open the door and kiss him again. _

\---

_ Assumption: Love doesn’t exist _

_ Proof: Sehun. _

_ Result: My assumption has been contradicted. Love exists, if only just for him _

_ \--- _

There is exactly one page left in Zitao’s notebook. It’s falling apart by now, it’s a wonder it’s held on for a decade. There is exactly one page left, and he knows what goes on it. 

_ Assumption: He’s going to say no _

_ Proof: I don’t think I’ve ever been this nervous before.  _

_ Result: ????? _

Eight hours later, in tiny print, after scrabbling for a pen and the notebook once Sehun has fallen asleep next to Zitao, after laughing happily and crying happily and being loved happily, Zitao scrawls the last words the notebook sees. 

_ He said yes. _

**Author's Note:**

> dfshjkasd !!! i hope everyone enjoyed me going on about maths and taohun ahhh have a nice day !!!!!  
You can find me on [Twitter](https://twitter.com/hztwsx) and also on [Tumblr](https://hztwsx.tumblr.com/).


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